Simplify the following expression: $q = \dfrac{4p^2 + 4p - 224}{p + 8} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $4$ , so we can rewrite the expression: $ q =\dfrac{4(p^2 + 1p - 56)}{p + 8} $ Then we factor the remaining polynomial: $p^2 + {1}p {-56} $ ${8} {-7} = {1}$ ${8} \times {-7} = {-56}$ $ (p + {8}) (p {-7}) $ This gives us a factored expression: $\dfrac{4(p + {8}) (p {-7})}{p + 8}$ We can divide the numerator and denominator by $(p - 8)$ on condition that $p \neq -8$ Therefore $q = 4(p - 7); p \neq -8$